On the sign structure of doped Mott insulators

TL;DR

This paper reveals that the sign structure of the doped Mott insulator's t-J model is fundamentally different from a Fermi gas, with a sparse, irreducible sign pattern indicating mutual statistics among quantum states.

Contribution

It uncovers a simplified, sparse sign structure in doped Mott insulators, contrasting with the complex signs in Fermi gases, and introduces a way to enumerate these signs.

Findings

Sign structure differs from Fermi gas

Signs can be gauged away at half-filling

Sparse 'irreducible' sign structure in doping regime

Abstract

We demonstrate that the sign structure of the t-J model on a hypercubic lattice is entirely different from that of a Fermi gas, by inspecting the high temperature expansion of the partition function up to all orders, as well as the multi-hole propagator of the half-filled state and the perturbative expansion of the ground state energy. We show that while the fermion signs can be completely gauged away by a Marshall sign transformation at half-filling, the bulk of the signs can be also gauged away in a doped case, leaving behind a rarified "irreducible" sign structure that can be enumerated easily by counting exchanges of holes with themselves and spins on their real space paths. Such a sparse sign structure implies a mutual statistics for the quantum states of the doped Mott insulator.